A brief History of Time pdfdrive com

FIGURE 7.4
A black hole with a mass a few times that of the sun would have a
temperature of only one ten millionth of a degree above absolute zero.
This is much less than the temperature of the microwave radiation that
fills the universe (about 2.7° above absolute zero), so such black holes
would emit even less than they absorb. If the universe is destined to go
on expanding forever, the temperature of the microwave radiation will
eventually decrease to less than that of such a black hole, which will
then begin to lose mass. But, even then, its temperature would be so low

---

that it would take about a million million million million million million
million million million million million years (1 with sixty-six zeros after
it) to evaporate completely. This is much longer than the age of the
universe, which is only about ten or twenty thousand million years (1 or
2 with ten zeros after it). On the other hand, as mentioned in
Chapter 6
,
there might be primordial black holes with a very much smaller mass
that were made by the collapse of irregularities in the very early stages
of the universe. Such black holes would have a much higher temperature
and would be emitting radiation at a much greater rate. A primordial
black hole with an initial mass of a thousand million tons would have a
lifetime roughly equal to the age of the universe. Primordial black holes
with initial masses less than this figure would already have completely
evaporated, but those with slightly greater masses would still be
emitting radiation in the form of X rays and gamma rays. These X rays
and gamma rays are like waves of light, but with a much shorter
wavelength. Such holes hardly deserve the epithet black: they really are
white hot and are emitting energy at a rate of about ten thousand
megawatts.
One such black hole could run ten large power stations, if only we
could harness its power. This would be rather difficult, however: the
black hole would have the mass of a mountain compressed into less than
a million millionth of an inch, the size of the nucleus of an atom! If you
had one of these black holes on the surface of the earth, there would be
no way to stop it from falling through the floor to the center of the
earth. It would oscillate through the earth and back, until eventually it
settled down at the center. So the only place to put such a black hole, in
which one might use the energy that it emitted, would be in orbit
around the earth—and the only way that one could get it to orbit the
earth would be to attract it there by towing a large mass in front of it,
rather like a carrot in front of a donkey. This does not sound like a very
practical proposition, at least not in the immediate future.
But even if we cannot harness the emission from these primordial
black holes, what are our chances of observing them? We could look for
the gamma rays that the primordial black holes emit during most of
their lifetime. Although the radiation from most would be very weak
because they are far away, the total from all of them might be
detectable. We do observe such a background of gamma rays:
Fig. 7.5

---

shows how the observed intensity differs at different frequencies (the
number of waves per second). However, this background could have
been, and probably was, generated by processes other than primordial
black holes. The dotted line in
Fig. 7.5
shows how the intensity should
vary with frequency for gamma rays given off by primordial black holes,
if there were on average 300 per cubic light-year. One can therefore say
that the observations of the gamma ray background do not provide any
positive evidence for primordial black holes, but they do tell us that on
average there cannot be more than 300 in every cubic light-year in the
universe. This limit means that primordial black holes could make up at
most one millionth of the matter in the universe.
With primordial black holes being so scarce, it might seem unlikely
that there would be one near enough for us to observe as an individual
source of gamma rays. But since gravity would draw primordial black
holes toward any matter, they should be much more common in and
around galaxies. So although the gamma ray background tells us that
there can be no more than 300 primordial black holes per cubic light-
year on average, it tells us nothing about how common they might be in
our own galaxy. If they were, say, a million times more common than
this, then the nearest black hole to us would probably be at a distance of
about a thousand million kilometers, or about as far away as Pluto, the
farthest known planet. At this distance it would still be very difficult to
detect the steady emission of a black hole, even if it was ten thousand
megawatts. In order to observe a primordial black hole one would have
to detect several gamma ray quanta coming from the same direction
within a reasonable space of time, such as a week. Otherwise, they might
simply be part of the background. But Planck’s quantum principle tells
us that each gamma ray quantum has a very high energy, because
gamma rays have a very high frequency, so it would not take many
quanta to radiate even ten thousand megawatts. And to observe these
few coming from the distance of Pluto would require a larger gamma ray
detector than any that have been constructed so far. Moreover, the
detector would have to be in space, because gamma rays cannot
penetrate the atmosphere.

---